Eugene Borisovich Dynkin (russian: link=no, Евгений Борисович Дынкин; 11 May 1924 – 14 November 2014) was a
Soviet
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national ...
and American
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
.
[ He made contributions to the fields of ]probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...
and algebra
Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathem ...
, especially semisimple
In mathematics, semi-simplicity is a widespread concept in disciplines such as linear algebra, abstract algebra, representation theory, category theory, and algebraic geometry. A semi-simple object is one that can be decomposed into a sum of ''sim ...
Lie group
In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the addit ...
s, Lie algebra
In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi iden ...
s, and Markov process
A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happen ...
es. The Dynkin diagram
In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line). Dynkin diagrams arise in the classification of semisimple Lie algebr ...
, the Dynkin system
A Dynkin system, named after Eugene Dynkin is a collection of subsets of another universal set \Omega satisfying a set of axioms weaker than those of -algebra. Dynkin systems are sometimes referred to as -systems (Dynkin himself used this term ...
, and Dynkin's lemma are named after him.
Biography
Dynkin was born into a Jew
Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""T ...
ish family, living in Leningrad
Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...
until 1935, when his family was exiled to Kazakhstan
Kazakhstan, officially the Republic of Kazakhstan, is a transcontinental country located mainly in Central Asia and partly in Eastern Europe. It borders Russia
Russia (, , ), or the Russian Federation, is a transcontinental coun ...
. Two years later, when Dynkin was 13, his father disappeared in the Gulag
The Gulag, an acronym for , , "chief administration of the camps". The original name given to the system of camps controlled by the State Political Directorate, GPU was the Main Administration of Corrective Labor Camps (, )., name=, group= ...
.[
]
Moscow University
At the age of 16, in 1940, Dynkin was admitted to Moscow University
M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...
. He avoided military service in World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great power ...
because of his poor eyesight, and received his MS in 1945 and his PhD PHD or PhD may refer to:
* Doctor of Philosophy (PhD), an academic qualification
Entertainment
* '' PhD: Phantasy Degree'', a Korean comic series
* ''Piled Higher and Deeper
''Piled Higher and Deeper'' (also known as ''PhD Comics''), is a newsp ...
in 1948. He became an assistant professor at Moscow, but was not awarded a "chair" until 1954 because of his political undesirability. His academic progress was made difficult due to his father's fate, as well as Dynkin's Jewish origin; the special efforts of Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Sovi ...
, his PhD supervisor, made it possible for Dynkin to progress through graduate school into a teaching position.[
]
USSR Academy of Sciences
In 1968, Dynkin was forced to transfer from the Moscow University to the Central Economic Mathematical Institute
The Central Economic Mathematical Institute (russian: Центральный экономико-математический институт (ЦЭМИ)) of the Russian Academy of Sciences is an economic research institute located in Moscow. It fo ...
of the USSR Academy of Sciences
The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991, uniting the country's leading scientists, subordinated directly to the Council of Ministers of the Soviet Union (until 1946 ...
.[ He worked there on the theory of economic growth and ]economic equilibrium
In economics, economic equilibrium is a situation in which economic forces such as supply and demand are balanced and in the absence of external influences the ( equilibrium) values of economic variables will not change. For example, in the st ...
.
Cornell
He remained at the Institute until 1976, when he emigrated to the United States
The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., federal district, five ma ...
. In 1977, he became a professor at Cornell University
Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to ...
.[
]
Death
Dynkin died at the Cayuga Medical Center in Ithaca, New York
New York most commonly refers to:
* New York City, the most populous city in the United States, located in the state of New York
* New York (state), a state in the northeastern United States
New York may also refer to:
Film and television
* '' ...
, aged 90. Dynkin was an atheist.
Mathematical work
Dynkin is considered to be a rare example of a mathematician who made fundamental contributions to two very distinct areas of mathematics: algebra
Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathem ...
and probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
. The algebraic period of Dynkin's mathematical work was between 1944 and 1954, though even during this time a probabilistic theme was noticeable. Indeed, Dynkin's first publication was in 1945, jointly with N. A. Dmitriev, solved a problem on the eigenvalue
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denot ...
s of stochastic matrices. This problem was raised at Kolmogorov's seminar on Markov chain
A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happen ...
s, while both Dynkin and Dmitriev were undergraduates.[
]
Lie Theory
While Dynkin was a student at Moscow University, he attended Israel Gelfand
Israel Moiseevich Gelfand, also written Israïl Moyseyovich Gel'fand, or Izrail M. Gelfand ( yi, ישראל געלפֿאַנד, russian: Изра́иль Моисе́евич Гельфа́нд, uk, Ізраїль Мойсейович Гел� ...
's seminar on Lie group
In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the addit ...
s. In 1944, Gelfand asked him to prepare a survey on the structure and classification of semisimple Lie groups, based on the papers by Hermann Weyl
Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is ass ...
and Bartel Leendert van der Waerden
Bartel Leendert van der Waerden (; 2 February 1903 – 12 January 1996) was a Dutch mathematician and historian of mathematics.
Biography
Education and early career
Van der Waerden learned advanced mathematics at the University of Amster ...
. Dynkin found the papers difficult to read, and in an attempt to better understand the results, he invented the notion of a "simple root" in a root system
In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties. The concept is fundamental in the theory of Lie groups and Lie algebras, especially the classification and representat ...
. He represented the pairwise angles between these simple roots in the form of a Dynkin diagram
In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line). Dynkin diagrams arise in the classification of semisimple Lie algebr ...
. In this way he obtained a cleaner exposition of the classification of complex semisimple Lie algebras. Of Dynkin's 1947 paper "Structure of semisimple Lie algebras", Bertram Kostant
Bertram Kostant (May 24, 1928 – February 2, 2017) was an American mathematician who worked in representation theory, differential geometry, and mathematical physics.
Early life and education
Kostant grew up in New York City, where he gradu ...
wrote:
Dynkin's 1952 influential paper "Semisimple subalgebras of semisimple Lie algebras", contained large tables and lists, and studied the subalgebras of the exceptional Lie algebras
Exception, exceptions or expectional may refer to:
*Exception (computer science), an anomalous condition during computation
* State of exception, a concept of extension of sovereign power
* Exceptional objects, in mathematics
** Exceptional iso ...
.
Probability theory
Dynkin is considered one of the founders of the modern theory of Markov process
A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happen ...
es. The results obtained by Dynkin and other participants of his seminar at Moscow University were summarized in two books. The first of these, "Theory of Markov Processes", was published in 1959, and laid the foundations of the theory.
Dynkin's one-hour talk at the 1962 International Congress of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU).
The Fields Medals, the Nevanlinna Prize (to be rename ...
in Stockholm, was delivered by Kolmogorov, since prior to his emigration, Dynkin was never permitted to travel to the West
West is a cardinal direction or compass point.
West or The West may also refer to:
Geography and locations
Global context
* The Western world
* Western culture and Western civilization in general
* The Western Bloc, countries allied with NATO ...
. This talk was titled "Markov processes and problems in analysis".
Prizes and awards
*Prize of the Moscow Mathematical Society, 1951
*Institute of Mathematical Statistics, Fellow, 1962
*American Academy of Arts and Sciences, Fellow, 1978
*National Academy of Sciences of the USA, Member, 1985
*American Mathematical Society, Leroy P. Steele Prize
The Leroy P. Steele Prizes are awarded every year by the American Mathematical Society, for distinguished research work and writing in the field of mathematics. Since 1993, there has been a formal division into three categories.
The prizes have ...
for Total Mathematical Work, 1993
*Moscow Mathematical Society, Honorary Member, 1995
*Doctor Honoris Causa of the Pierre and Marie Curie University (Paris 6), 1997
*Doctor of Science (honoris causa) of the University of Warwick
, mottoeng = Mind moves matter
, established =
, type = Public research university
, endowment = £7.0 million (2021)
, budget = £698.2 million (202 ...
, 2003.
*Doctor Honoris Causa of the Independent Moscow University (Russia), 2003
*Fellow of the American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings ...
, 2012
Publications
*
*
*
*
*
*
*
*
See also
;Algebra:
* Affine Dynkin diagram
*Coxeter–Dynkin diagram
In geometry, a Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes). It describes ...
*Dynkin index In mathematics, the Dynkin index I() of a finite-dimensional highest-weight representation of a compact simple Lie algebra \mathfrak g with highest weight \lambda is defined by
\text_= 2I(\lambda) \text_,
where V_0 is the 'defining representati ...
* Dynkin–Specht–Wever Lemma
;Probability:
*Dynkin's formula
In mathematics — specifically, in stochastic analysis — Dynkin's formula is a theorem giving the expected value of any suitably smooth statistic of an Itō diffusion at a stopping time. It may be seen as a stochastic generalization o ...
*Dynkin system
A Dynkin system, named after Eugene Dynkin is a collection of subsets of another universal set \Omega satisfying a set of axioms weaker than those of -algebra. Dynkin systems are sometimes referred to as -systems (Dynkin himself used this term ...
Notes
External links
*
*
Department listing at Cornell University
Personal web page
Collection of interviews assembled by Dynkin
{{DEFAULTSORT:Dynkin, Eugene B.
1924 births
2014 deaths
Jewish American atheists
Fellows of the American Mathematical Society
Members of the United States National Academy of Sciences
20th-century Russian mathematicians
20th-century American mathematicians
21st-century American mathematicians
Soviet mathematicians
Cornell University faculty
Russian atheists
Russian Jews
Mathematicians from Saint Petersburg
Algebraists
Probability theorists
Soviet emigrants to the United States
Moscow State University alumni
People from Saint Petersburg
Measure theorists